Statistics of Nucleation and Growth of Single Monolayers in Nanowires: Towards a Deterministic Regime

The vapor-liquid-solid growth of semiconductor nanowires proceeds via the sequential nucleation and extension of biatomic monolayers at the interface between the solid wire and a liquid catalyst nanodroplet. In the case of III-V compounds, this mother phase contains only a small concentration of the volatile group V atoms. The growth regime where there is not enough such atoms available in the liquid at nucleation to complete a whole monolayer is studied experimentally and theoretically. Each monolayer cycle then consists in the rapid formation of a partial monolayer, followed by a slower propagation stage and by a waiting time preceding the next nucleation. The propagation and waiting times of long sequences of monolayers are measured in situ in a transmission electron microscope at three growth temperatures, in a single GaAs nanowire. The process is modeled and the statistics of the characteristic times are computed numerically and analytically. At low temperature, the weakness of group V desorption from the liquid should lead to a constant total monolayer cycle time, despite the stochasticity of the nucleation events. The modeling of the experiments yields values of several crucial growth parameters and provides guidance for the growth of nanowires in a deterministic regime.